Welcome to the world, baby Eric! Thank goodness you were born on Valentine’s Day, the international Day Of Love. When your Dad has, in the past, been described as ‘TV’s Mr Nasty’, you’re going to need all the love you can get your tiny hands on.

We’re all desperate to know whether Simon Cowell will be a good dad. So far, the signs are promising. He could have called his new baby Pineapple, or Middle Eight, or Zeus - but he plumped for Eric, after his own dear old Dad. Solid, traditional, reassuring. And baby Eric will grow up knowing that he could become a superhero and save the world, if he just eats enough bananas.

Or he could fall in love with a beautiful mermaid who will want to be with him so badly, she’ll lose her tail and live on land forever. However, Twitter wags have been quick to point out that when little Eric starts school, he’ll be plagued on the playground by shouts of “Twit twoooooo!” Eric Cowell. Say it aloud. Eric Owl.

But baby Eric’s future pals will need to be nice to him if they’re going to survive on playdates with the heir to the BGT fortune. It’s all too easy to imagine the mogul drawing himself up to his full height and telling a weeping toddler “you have the personality of a handle”.

(Photo: Jae Donnelly)

Cowell is straight from the school of “say what you see” criticism, which makes for great TV - but it might make things awkward when young Eric just wants Daddy to tell him how much he likes his latest finger painting.

Also, Cowell is a legendary neat freak. This is a man who had parts of a house rebuilt because the brickwork wasn’t neat enough. A man who would pay for not quite symmetrical trees to be ripped out of the ground and repositioned. A man who has issued specifications about the colour his bog roll should be. Does he know how often babies are sick?

Does he realise that babies love drinking warm milk, and love spilling, throwing and playing with warm milk even more, and will leave stinky, sticky messes all over his favourite pricey cushions? And we haven’t even got to ground up rusks in the carpet, crayons on walls and dirty nappies.

I’m sure the most appallingly off key, inappropriately dressed, dull wannabe in the world would not disgust Simon as much as a pile of poo filled Pampers. Sure, Simon has staff, but when it comes to your kid, you shouldn’t be outsourcing your duties, otherwise you’ll end up with a scary, stern, Victorian relationship with your child. However, Simon should excel when it comes to bathtime.

Even if Simon can get through Eric’s teething years, he might struggle when his son reaches his teens.

As a pop mogul, how will he manage if Eric has an “alternative” phase? He might be a cute baby, but it’s all too easy to imagine him banging doors, covered in tattoos and piercings, screaming “**** YOU! I’M NOT GONNA DO WHAT YOU TELL ME!” the hook line from Killing In The Name, the Rage Against The Machine song used in a campaign to keep Cowell’s X Factor prodigy little Joe McElderry from hitting the top chart spot.

And when his Dad is a dedicated perfectionist with incredibly high standards, Eric will have a lot to rebel against.

Ultimately, fatherhood is a challenge no matter who you are. It’s also an adventure. Simon Cowell might be wealthy and powerful, but he’ll struggle in the same way that every new Dad does.

However, he’s in a brilliant position to provide for baby Eric, and there’s no doubt that he’ll find the experience rewarding as well as frustrating, and father and son will both grow and learn along the way. We congratulate Simon and Lauren, and wish them both lots of love and luck.

And Simon, if you’re reading, babies’ nappies just need to cover their bums. They don’t need to go all the way up to the top of their armpits.